@Msfolly Yes, laggiù seems appropriate if you want to convey the idea of a distance between where you are at the moment of speaking and the place you're asking about.

@Msfolly glad to be of some help!

@Mrs_MG Sorry for my tardiness. The quoted sentence is not correct from a grammatical point of view: as Msfolly noticed in her first comment to my answer, and as she later found out, there's a missing che. Also, as I said, en is not an Italian preposition: it might have been an in. A correct alternative for asking «(But,) what's the weather like over there in January?» is: «Che tempo fa lì ~~*en*~~ in gennaio?», where en should be cancelled. And yes, languages are really fun! :)

@DaG you're right: it is not necessary, but it's more like a personal choice. Also, there are several examples of its use.

@Mrs_MG, I'm not sure I've fully understood your question. Are you asking why the correspondence between the Italian sentence "Ma, fa tempo lì en gennaio?" and the English sentence "What's the weather like in January?" is not exact?

@DigitalVeer You're very welcome! And thanks to you too! :)